Abstract

Phase images of the human brain acquired using gradient echo based Magnetic Resonance Imaging techniques show excellent contrast at 7T. This contrast is attributed to small variations in magnetic susceptibility that perturb the main magnetic field and thus yield a spatial variation of the NMR frequency. The work described in this thesis is primarily concerned with mapping the distribution of magnetic susceptibility within the human brain using these phase images. The main technical challenges of the project were first to extract accurate field maps based on phase data, and then to solve the ill-posed problem of inverting these field maps to reconstruct susceptibility (ϰ) maps.

In initial work, simulations of field shifts based on known ϰ -distributions are compared to field maps acquired in vivo to highlight the non-local relationship between measured field offsets and the underlying susceptibility. These simulations were carried out using a recently derived Fourier method.

The bulk of the thesis is then devoted to a detailed study of the process of inverting field maps generated from phase data using the Fourier relationship to yield quantitative 3D ϰ -maps. Unfortunately, the inversion problem is ill-posed and requires careful conditioning, either through rotation of the sample being imaged or through regularisation. A simple k-space threshold is introduced to condition the inversion and the preliminary results of applying this method to brain data from healthy subjects and patients with Parkinson's disease and multiple sclerosis are presented. The results suggest that susceptibility mapping is sensitive to iron deposition and could be a useful tool in investigating the progression of neurodegeneratived diseases.

Iterative inversion algorithms, which deal with noise more robustly and allow more sophisticated filtering techniques to be employed, are then presented. These powerful regularisation methods are compared to previously described techniques, and are shown to yield high quality whole-brain ϰ -maps.